Nonlinear dynamics of semiconductor lasers under individually optoelectronic feedback (OEF) and optical feedback (OF) is attracted much attention in these two decades. However, according to my knowledge, there is no related research results in dual-feedback system composed of optical and optoelectronic feedbacks. In this paper, the nonlinear dynamics of the dual-feedback system is studied and applications in generation of broadband chaos and stabilized pulses based on quasi-periodic (QP) states are achieved. Generally, QP states do not have contributed application which limited the research attention in recent years. Here we focused on the QP state and turned it to be the useful chaos and pulses. The QP is firstly generated by pure OEF system and then applying an additional OF system to obtain the chaos and pulses by tuning the controllable conditions of feedback strength and delay time. To explore the rich dynamics of the dual feedback system, mappings of each dynamical states are calculated, including regular pulsing, periodic oscillation, and chaotic oscillation and pulsing states. Furthermore, chaos bandwidth and amplitude variation of regular pulses are examined to quantify the signals generated. A 2-fold improvement of chaotic oscillation frequency is observed in dual feedback system compared to the chaos generated by pure OEF system. Broadband bandwidth of chaotic oscillation is obtained in dual-feedback system when using a relaxation oscillation frequency of 2.5 GHz laser in the free-running condition. Moreover, the improved percentage of averaged amplitude variation in regular pulses is around 81.6% compared to those generated by pure OEF scheme.